The Consensus Number One?

3 min readJul 2, 2020
Moulay Abd-er-Rahman, Sultan of Morocco Leaving the Palace in Meknès with his Entourage, by DeLacroix, Ferdinand-Victor-Eugène

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I’ve just received from one of my readers a reference to the “The Consensus Number of a Cryptocurrency” work co-authored by Rachid Guerraoui as well as a number of others.

It turns to be a curious piece, specially, considering that Mr. Guerraoui — a professor at the School of Computer and Communication Sciences at Ecole Polytechnique Fédérale de Lausanne (EPFL) (see below) — has distinguished himself not only on the field of concurrent and distributed computing but also in Moroccan politics as well.


I’ve spend less that 30 minutes looking into this paper, so I might have grossly disregarded some of its important aspects, but what caught my attention right from the start is the following.

Citing: “We first consider the problem as defined by Nakamoto, where
only a single process — the account owner — can withdraw from each

Anyone familiar with ‘Bitcoin: A Peer-to-Peer Electronic Cash System’ knows that the word ‘account’ is never mentioned by its author on all entirety of 8 pages. Moreover, it’s, famously, not necessary because the Bitcoin protocol realization, proposed by Satochi, is based on transactions (UTXO) — not on accounts.

Might it be that Pr. Guerraoui has not read it or deliberately disregarded this obvious fact and just used Nakomoto’s work in order to attract attention to his own proposition? I wouldn’t dare to suggest that, of course.

As to proposition itself it goes as following:

Citing: “Bitcoin and numerous follow-up systems typically assume that total order — and thus consensus — is vital to preventing double-spending. There seems to be a common belief, indeed, that a consensus algorithm is essential for implementing decentralized asset transfers. As our main result in this paper, we show that this belief is false. We do so by casting the asset transfer problem as a sequential object type and determining that it has consensus number 1 in Herlihy’s hierarchy”.

Maurice Herlihy — distinguished Professor of Computer Science at Brown University — is known for his researches in the area of so-called “wait-free synchronization” used (among others) in a memory architecture.

Extract (Maurice Herlihy’s ‘Wait-Free Synchronization’): “A wait-free implementation of a concurrent data object is one that guarantees that any process can complete any operation in a finite number of steps, regardless of the execution speeds of the other processes.”

In case of blockchain it can be applied to improve transactions throughput — not to deals with its falsifiability. Taking Pr. Herlihy work one step further in this direction is how Pr. Guerraoui and others attempt to contribute to the fields of crypto-currencies consensus algorithms.

Extract: “An asset transfer object maintains a set of accounts. Each account is associated with an owner process that is the only one allowed to issue transfers withdrawing from this account. Every process can however read the balance of any account. The main insight here is that relating accounts to unique owners obviates the need for consensus. It is the owner that decides on the order of transfers from its own account, without the need to agree with any other process — thus the consensus number 1. Other processes only validate the owner’s decisions, ensuring that causal relations across accounts are respected.”

As I’ve mentioned earlier, because I’ve not been diligent enough in my preliminary researches I can’t definitely state that not only the proposed by Pr. Guerraoui architecture is very reminiscent of that of DAGs but also that maintaining ‘the order of transfers’ trough all the system alleviated by ‘an owner process’ maintaining each account will not contribute positively to overall system performance and only leads to its imminent centralization.



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